A standard exam question gives you a failed result and asks for reasons. Work from the plate backwards.
No colonies at all. Either nothing was taken up or everything died. Check that the host cells were competent, that the heat shock or electroporation step was done correctly, that the cells were allowed a recovery period before being plated on antibiotic, and that the antibiotic concentration was not too high. Also check the obvious: that the plasmid carries resistance to the antibiotic you used.
Plenty of colonies, but all non-recombinant. The vector re-closed on itself. This is why cut vector is usually treated to remove its terminal phosphates, so the two ends cannot be joined without an insert bridging them. Too little insert relative to vector does the same thing.
Colonies on the no-insert control plate. The control is there precisely to reveal this. A heavy lawn on it means your vector preparation was incompletely digested, so uncut circular vector is transforming at high efficiency.
Colonies that look right but the insert is wrong. Partial digestion, star activity from over-digestion, or contaminating DNA. This is exactly what the diagnostic digest and sequencing stages are for.
Always run the controls. Vector with no insert, and cells with no DNA. Without them a failed experiment cannot be diagnosed, and an answer that omits them is incomplete however good the rest is.